Given the following partial dp array after processing some elements of arr, where dp[w] indicates if sum w is achievable: Index: 0 1 2 3 4 5 6 7 8 9 10 Value: T F T F T F F F F F F If total_sum = 10, which of the following could be the original input array?

hard🔄 Reverse Engineer Q9 of Q15

Dynamic Programming: Knapsack - Minimum Subset Sum Difference

A[2, 4, 6]

B[1, 2, 3]

C[5, 5]

D[1, 3, 4]

Step-by-Step Solution

Solution:

Step 1: Analyze achievable sums
dp shows sums 0,2,4 achievable (T), others false.
Step 2: Check which array can produce these sums
[2,4,6] can produce sums 0,2,4 by choosing 2 or 4 alone or none.
Step 3: Verify other options
[1,3,4] can produce sum 1,3,4 which is not reflected; [5,5] only 0,5,10; [1,2,3] produces sums 1,2,3, etc.
Final Answer:
Option A -> Option A
Quick Check:
dp matches sums achievable by [2,4,6] subset [OK]

Quick Trick: Check achievable sums against subset sums of candidate arrays [OK]

Common Mistakes:

MISTAKES

Ignoring sums not achievable
Assuming all sums possible

Trap Explanation:

PITFALL

Candidates pick arrays with sums close but not matching dp achievable sums.

Interviewer Note:

CONTEXT

Tests deep understanding of dp state and subset sums.

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More Dynamic Programming: Knapsack Quizzes

Given the following partial dp array after processing some elements of arr, where dp[w] indicates if sum w is achievable: Index: 0 1 2 3 4 5 6 7 8 9 10 Value: T F T F T F F F F F F If total_sum = 10, which of the following could be the original input array?

Step 1: Analyze achievable sums

Step 2: Check which array can produce these sums

Step 3: Verify other options

Final Answer:

Quick Check:

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